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Simplifying LogX + Log(X + 6) = Log(12X) Reorder the terms: goLX + goL(6 + X) = Log(12X) goLX + (6 * goL + X * goL) = Log(12X) goLX + (6goL + goLX) = Log(12X) Reorder the terms: 6goL + goLX + goLX = Log(12X) Combine like terms: goLX + goLX = 2goLX 6goL + 2goLX = Log(12X) Remove parenthesis around (12X) 6goL + 2goLX = goL * 12X Reorder the terms for easier multiplication: 6goL + 2goLX = 12goL * X Multiply goL * X 6goL + 2goLX = 12goLX Solving 6goL + 2goLX = 12goLX Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12goLX' to each side of the equation. 6goL + 2goLX + -12goLX = 12goLX + -12goLX Combine like terms: 2goLX + -12goLX = -10goLX 6goL + -10goLX = 12goLX + -12goLX Combine like terms: 12goLX + -12goLX = 0 6goL + -10goLX = 0 Factor out the Greatest Common Factor (GCF), '2goL'. 2goL(3 + -5X) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'goL' equal to zero and attempt to solve: Simplifying goL = 0 Solving goL = 0 Move all terms containing g to the left, all other terms to the right. Simplifying goL = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3 + -5X)' equal to zero and attempt to solve: Simplifying 3 + -5X = 0 Solving 3 + -5X = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5X = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5X = 0 + -3 -5X = 0 + -3 Combine like terms: 0 + -3 = -3 -5X = -3 Add '5X' to each side of the equation. -5X + 5X = -3 + 5X Combine like terms: -5X + 5X = 0 0 = -3 + 5X Simplifying 0 = -3 + 5X The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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